Resources for Projects
This page will provide links to papers and other resources that may be useful to you as you start to think about your projects. Still, I am sure that most people will be finding their own "resource paper."
We'll see how this evolves, but I expect to put up papers on a regular basis. You can also suggest candidates that you think would be of interest to class members.
I will be adding papers as I think of them, so here is no structure to this page beyond chronological order of entry. Easy things, hard things, old things or new things can occur in any order.
Garsia (1976) "Combinatorial Inequalities and Smoothness of Functions"
This is a lovely (and leisurely) exposition of results that show an elegant interplay of combinatorics and mathematical analysis. Specifically, it show how you can get "smoothness" information out of a certain "average smoothness" information. Don't be put off if you happen not to know some of the words used in the first few pages of the paper. If you scan the whole thing I think you'll see why I like it.
Blei (1983) "An Elementary Proof of the Grothendieck Inequality"
This is a paper of resplendent beauty. It is also packed with "news you can use." First, the Grothendieck Inequality is in itself very much worth knowing. Second, Blei's technique carries a seed of great generality. Finally, if you take a step behind Blei's specific formulas you will see a philosophy of iteration which once mastered almost forces one to feel stronger mathematically.
Zinkevich (2003) "On-Line Convex Programming and Generalized Infinitesimal Gradient Ascent"
The theory of on-line algorithms tasks the solver with making a sequence of choice as "new data" is presented. Some of the theorems in this subject are very paradoxical when first met since they assert that a person working on-line can do almost as well as a person will full knowledge of the future. We'll see several examples of this in class, but Zinkevich (2003) is a very "pure play" example. You can master this paper in a couple of days, but the attending literature has exploded.
We I first met the paper, I was sure that I had an "engine" on my hands, but it turns out that the theory of on-line optimization has a little caginess in the formulation. This is not the kind of weapon that I hoped it would be, but it is very nice to know and it can be used to prove some other things. You might try proving Frakas's Lemma or LP Duality using Zinkevich's algorithm!
Shepp (1967) "Explicit Solutions to Some Problems of Optimal Stopping"
Students are not often eager to read papers that are older than they are, and that is mostly a good idea. Still, from time to time, one should read a classic. This one is squarely in the domain of this course, though we'll spend a bit more time on discrete time problems. If you want to do just a piece of this paper, you could look at the section on Wald's identity or the section on smooth fit.